mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-11-14 10:39:05 +00:00
439 lines
17 KiB
C++
439 lines
17 KiB
C++
#ifndef SPROUT_RANDOM_BINOMIAL_DISTRIBUTION_HPP
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#define SPROUT_RANDOM_BINOMIAL_DISTRIBUTION_HPP
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#include <cmath>
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#include <iosfwd>
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#include <istream>
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#include <sprout/config.hpp>
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#include <sprout/array.hpp>
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#include <sprout/random/random_result.hpp>
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#include <sprout/random/uniform_01.hpp>
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namespace sprout {
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namespace random {
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namespace detail {
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template<typename RealType>
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struct binomial_table {
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public:
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SPROUT_STATIC_CONSTEXPR sprout::array<RealType, 10> table = sprout::array<RealType, 10>{{
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0.08106146679532726,
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0.04134069595540929,
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0.02767792568499834,
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0.02079067210376509,
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0.01664469118982119,
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0.01387612882307075,
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0.01189670994589177,
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0.01041126526197209,
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0.009255462182712733,
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0.008330563433362871
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}};
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};
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template<class RealType>
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SPROUT_CONSTEXPR sprout::array<RealType, 10> sprout::random::detail::binomial_table<RealType>::table;
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} // namespace detail
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//
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// binomial_distribution
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//
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template<typename IntType = int, typename RealType = double>
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class binomial_distribution {
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public:
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typedef RealType input_type;
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typedef IntType result_type;
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private:
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struct btrd_type {
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public:
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RealType r;
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RealType nr;
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RealType npq;
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RealType b;
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RealType a;
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RealType c;
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RealType alpha;
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RealType v_r;
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RealType u_rv_r;
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};
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private:
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static SPROUT_CONSTEXPR bool arg_check_nothrow(IntType t_arg, RealType p_arg) {
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return t_arg >= IntType(0) && RealType(0) <= p_arg && p_arg <= RealType(1);
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}
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static SPROUT_CONSTEXPR IntType arg_check(IntType t_arg, RealType p_arg) {
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return arg_check_nothrow(t_arg, p_arg)
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? t_arg
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: throw "assert(t_arg >= IntType(0) && RealType(0) <= p_arg && p_arg <= RealType(1))"
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;
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}
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public:
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//
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// param_type
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//
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class param_type {
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public:
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typedef binomial_distribution distribution_type;
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private:
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IntType t_;
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RealType p_;
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public:
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SPROUT_CONSTEXPR param_type()
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: t_(1)
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, p_(0.5)
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{}
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SPROUT_CONSTEXPR explicit param_type(IntType t_arg, RealType p_arg = RealType(0.5))
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: t_(arg_check(t_arg, p_arg))
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, p_(p_arg)
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{}
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SPROUT_CONSTEXPR IntType t() const {
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return t_;
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}
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SPROUT_CONSTEXPR RealType p() const {
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return p_;
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}
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template<typename Elem, typename Traits>
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friend std::basic_ostream<Elem, Traits>& operator>>(
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std::basic_istream<Elem, Traits>& lhs,
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param_type const& rhs
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)
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{
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IntType t;
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RealType p;
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if (lhs >> t >> std::ws >> p) {
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if (arg_check_nothrow(t, p)) {
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rhs.t_ = t;
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rhs.p_ = p;
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} else {
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lhs.setstate(std::ios_base::failbit);
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}
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}
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return lhs;
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}
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template<typename Elem, typename Traits>
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friend std::basic_ostream<Elem, Traits>& operator<<(
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std::basic_ostream<Elem, Traits>& lhs,
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param_type const& rhs
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)
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{
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return lhs << rhs.t_ << " " << rhs.p_;
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}
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SPROUT_CONSTEXPR friend bool operator==(param_type const& lhs, param_type const& rhs) {
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return lhs.t_ == rhs.t_ && lhs.p_ == rhs.p_;
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}
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SPROUT_CONSTEXPR friend bool operator!=(param_type const& lhs, param_type const& rhs) {
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return !(lhs == rhs);
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}
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};
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private:
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static SPROUT_CONSTEXPR IntType init_t(IntType t) {
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return t;
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}
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static SPROUT_CONSTEXPR RealType init_p(RealType p) {
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return RealType(0.5) < p ? 1 - p : p;
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}
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static SPROUT_CONSTEXPR IntType init_m(IntType t, RealType p) {
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return static_cast<IntType>((init_t(t) + 1) * init_p(p));
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_6(IntType t, RealType p, RealType r, RealType nr, RealType npq, RealType b, RealType a, RealType c, RealType alpha, RealType v_r) {
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return btrd_type {
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r,
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nr,
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npq,
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b,
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a,
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c,
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alpha,
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v_r,
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RealType(0.86) * v_r
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};
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_5(IntType t, RealType p, RealType r, RealType nr, RealType npq, RealType sqrt_npq, RealType b) {
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return init_btrd_6(t, p, r, nr, npq, b, RealType(-0.0873) + RealType(0.0248) * b + RealType(0.01) * p, t * p + RealType(0.5), (RealType(2.83) + RealType(5.1) / b) * sqrt_npq, RealType(0.92) - RealType(4.2) / b);
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_4(IntType t, RealType p, RealType r, RealType nr, RealType npq, RealType sqrt_npq) {
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return init_btrd_5(t, p, r, nr, npq, sqrt_npq, RealType(1.15) + RealType(2.53) * sqrt_npq);
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_3(IntType t, RealType p, RealType r, RealType nr, RealType npq) {
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using std::sqrt;
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return init_btrd_4(t, p, r, nr, npq, sqrt(npq));
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_2(IntType t, RealType p, RealType r) {
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return init_btrd_3(t, p, r, (t + 1) * r, t * p * (1 - p));
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_1(IntType t, RealType p) {
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return init_btrd_2(t, p, p / (1 - p));
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd(IntType t, RealType p) {
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return init_btrd_1(init_t(t), init_p(p));
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}
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static SPROUT_CONSTEXPR RealType init_q_n(IntType t, RealType p) {
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using std::pow;
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return pow(1 - init_p(p), static_cast<RealType>(init_t(t)));
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}
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static SPROUT_CONSTEXPR bool init_use_inversion(IntType t, RealType p) {
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return init_m(t, p) < 11;
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}
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static SPROUT_CONSTEXPR RealType fc_1(RealType ikp1) {
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return (RealType(1) / 12 - (RealType(1) / 360 - (RealType(1) / 1260) * (ikp1 * ikp1)) * (ikp1 * ikp1)) * ikp1;
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}
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static SPROUT_CONSTEXPR RealType fc(IntType k) {
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return k < 10
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? sprout::random::detail::binomial_table<RealType>::table[k]
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: fc_1(RealType(1) / (k + 1))
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;
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}
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private:
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IntType t_;
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RealType p_;
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IntType m_;
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btrd_type btrd_;
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RealType q_n_;
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private:
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SPROUT_CONSTEXPR bool use_inversion() const {
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return m_ < 11;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert_4(Engine const& eng, RealType u, RealType q, RealType s, RealType a, RealType r, IntType x = 0) const {
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return u > r
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? invert_4(eng, u - r, q, s, a, ((a / (x + 1)) - s) * r, x + 1)
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: sprout::random::random_result<Engine, binomial_distribution>(x, eng, *this)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert_3(IntType t, Engine const& eng, RealType u, RealType q, RealType s) const {
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return invert_4(eng, u, q, s, (t + 1) * s, q_n_);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert_2(IntType t, RealType p, Engine const& eng, RealType u, RealType q) const {
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return invert_3(t, eng, u, q, p / q);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert_1(IntType t, RealType p, Engine const& eng, RealType u) const {
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return invert_2(t, p, eng, u, 1 - p);
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert_0(IntType t, RealType p, Random const& rnd) const {
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return invert_1(t, p, rnd.engine(), rnd.result());
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert(IntType t, RealType p, Engine const& eng) const {
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return invert_0<Engine>(t, p, sprout::random::uniform_01<RealType>()(eng));
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert2_0(IntType t, sprout::random::random_result<Engine, binomial_distribution> const& rnd) const {
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return sprout::random::random_result<Engine, binomial_distribution>(t - rnd.result(), rnd.engine(), rnd.distribution());
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> invert2(IntType t, RealType p, Engine const& eng) const {
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return invert2_0<Engine>(t, invert(t, p, eng));
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_10(Engine const& eng, RealType v, IntType k, IntType nm, RealType h, IntType nk) const {
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using std::log;
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return v <= h + (t_ + 1) * log(static_cast<RealType>(nm) / nk) + (k + RealType(0.5)) * log(nk * btrd_.r / (k + 1))- fc(k)- fc(t_ - k)
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? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
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: generate(eng)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_9(Engine const& eng, RealType v, IntType k, IntType nm) const {
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using std::log;
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return generate_10(eng, v, k, nm, (m_ + RealType(0.5)) * log((m_ + 1) / (btrd_.r * nm)) + fc(m_) + fc(t_ - m_), t_ - k + 1);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_8(Engine const& eng, RealType v, IntType k, RealType rho, RealType t) const {
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return v < t - rho ? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
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: v > t + rho ? generate(eng)
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: generate_9(eng, v, k, t_ - m_ + 1)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_7_3(Engine const& eng, RealType v, IntType k, RealType f) const {
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return v <= f
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? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
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: generate(eng)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_7_2(Engine const& eng, RealType v, IntType k, RealType f, IntType i) const {
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return i != k
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? generate_7_2(eng, v * (btrd_.nr / (i + 1) - btrd_.r), k, f, i + 1)
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: generate_7_3(eng, v, k, f)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_7_1(Engine const& eng, RealType v, IntType k, RealType f, IntType i) const {
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return i != k
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? generate_7_1(eng, v, k, f * (btrd_.nr / (i + 1) - btrd_.r), i + 1)
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: generate_7_3(eng, v, k, f)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_7(Engine const& eng, RealType v, IntType k, RealType f = RealType(1)) const {
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return m_ < k ? generate_7_1(eng, v, k, f * (btrd_.nr / (m_ + 1) - btrd_.r), m_ + 1)
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: m_ > k ? generate_7_2(eng, v * (btrd_.nr / (k + 1) - btrd_.r), k, f, k + 1)
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: generate_7_3(eng, v, k, f)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_6(Engine const& eng, RealType v, IntType k, RealType km) const {
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using std::log;
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return km <= 15
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? generate_7(eng, v, k)
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: generate_8(eng, log(v), k, (km / btrd_.npq) * (((km / RealType(3.0) + RealType(0.625)) * km + RealType(1.0) / 6) / btrd_.npq + RealType(0.5)), -km * km / (2 * btrd_.npq))
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_5(Engine const& eng, RealType v, RealType u, RealType us, IntType k) const {
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using std::abs;
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return k < 0 || k > t_
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? generate(eng)
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: generate_6(eng, v * btrd_.alpha / (btrd_.a / (us * us) + btrd_.b), k, abs(k - m_))
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_4(Engine const& eng, RealType v, RealType u, RealType us) const {
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using std::floor;
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return generate_5(eng, v, u, us, static_cast<IntType>(floor((2 * btrd_.a / us + btrd_.b) * u + btrd_.c)));
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_3(Engine const& eng, RealType v, RealType u) const {
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using std::abs;
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return generate_4(eng, v, u, 0.5 - abs(u));
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_2(Random const& rnd, RealType v) const {
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return v >= btrd_.v_r
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? generate_3(
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rnd.engine(),
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v,
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rnd.result() - RealType(0.5)
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)
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: generate_3(
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rnd.engine(),
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rnd.result() * btrd_.v_r,
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((v / btrd_.v_r - RealType(0.93)) < 0 ? RealType(-0.5) : RealType(0.5)) - (v / btrd_.v_r - RealType(0.93))
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)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_1_1(Engine const& eng, RealType u) const {
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using std::floor;
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using std::abs;
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return sprout::random::random_result<Engine, binomial_distribution>(
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static_cast<IntType>(floor((2 * btrd_.a / (RealType(0.5) - abs(u)) + btrd_.b) * u + btrd_.c)),
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eng,
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*this
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);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_1(Engine const& eng, RealType v) const {
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return v <= btrd_.u_rv_r
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? generate_1_1(eng, v / btrd_.v_r - RealType(0.43))
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: generate_2<Engine>(sprout::random::uniform_01<RealType>()(eng), v)
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;
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_0(Random const& rnd) const {
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return generate_1(rnd.engine(), rnd.result());
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate(Engine const& eng) const {
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return generate_0<Engine>(sprout::random::uniform_01<RealType>()(eng));
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate2_0(IntType t, sprout::random::random_result<Engine, binomial_distribution> const& rnd) const {
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return sprout::random::random_result<Engine, binomial_distribution>(t - rnd.result(), rnd.engine(), rnd.distribution());
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate2(IntType t, Engine const& eng) const {
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return generate2_0<Engine>(t, generate(eng));
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}
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void init() {
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m_ = init_m(t_, p_);
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if (use_inversion()) {
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q_n_ = init_q_n(t_, p_);
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} else {
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btrd_ = init_btrd(t_, p_);
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}
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}
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public:
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SPROUT_CONSTEXPR binomial_distribution()
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: t_(1)
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, p_(RealType(0.5))
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, m_(init_m(1, RealType(0.5)))
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, btrd_(!init_use_inversion(1, RealType(0.5)) ? init_btrd(1, RealType(0.5)) : btrd_type())
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, q_n_(init_use_inversion(1, RealType(0.5)) ? init_q_n(1, RealType(0.5)) : RealType())
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{}
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SPROUT_CONSTEXPR explicit binomial_distribution(IntType t_arg, RealType p_arg = RealType(0.5))
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: t_(arg_check(t_arg, p_arg))
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, p_(p_arg)
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, m_(init_m(t_arg, p_arg))
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, btrd_(!init_use_inversion(t_arg, p_arg) ? init_btrd(t_arg, p_arg) : btrd_type())
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, q_n_(init_use_inversion(t_arg, p_arg) ? init_q_n(t_arg, p_arg) : RealType())
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{}
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SPROUT_CONSTEXPR explicit binomial_distribution(param_type const& parm)
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: t_(parm.t())
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, p_(parm.p())
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, m_(init_m(parm.t(), parm.p()))
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, btrd_(!init_use_inversion(parm.t(), parm.p()) ? init_btrd(parm.t(), parm.p()) : btrd_type())
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, q_n_(init_use_inversion(parm.t(), parm.p()) ? init_q_n(parm.t(), parm.p()) : RealType())
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{}
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SPROUT_CONSTEXPR result_type t() const {
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return t_;
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}
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|
SPROUT_CONSTEXPR result_type p() const {
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|
return p_;
|
|
}
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|
SPROUT_CONSTEXPR result_type min() const {
|
|
return 0;
|
|
}
|
|
SPROUT_CONSTEXPR result_type max() const {
|
|
return t_;
|
|
}
|
|
SPROUT_CONSTEXPR param_type param() const {
|
|
return param_type(t_, p_);
|
|
}
|
|
void param(param_type const& parm) {
|
|
t_ = parm.a();
|
|
p_ = parm.b();
|
|
init();
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> operator()(Engine const& eng) const {
|
|
return use_inversion() ? RealType(0.5) < p_
|
|
? invert2(t_, 1 - p_, eng)
|
|
: invert(t_, p_, eng)
|
|
: RealType(0.5) < p_ ? generate2(t_, eng)
|
|
: generate(eng)
|
|
;
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend std::basic_ostream<Elem, Traits>& operator>>(
|
|
std::basic_istream<Elem, Traits>& lhs,
|
|
binomial_distribution const& rhs
|
|
)
|
|
{
|
|
param_type parm;
|
|
lhs >> parm;
|
|
param(parm);
|
|
return lhs;
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend std::basic_ostream<Elem, Traits>& operator<<(
|
|
std::basic_ostream<Elem, Traits>& lhs,
|
|
binomial_distribution const& rhs
|
|
)
|
|
{
|
|
return lhs << param();
|
|
}
|
|
SPROUT_CONSTEXPR friend bool operator==(binomial_distribution const& lhs, binomial_distribution const& rhs) {
|
|
return lhs.param() == rhs.param();
|
|
}
|
|
SPROUT_CONSTEXPR friend bool operator!=(binomial_distribution const& lhs, binomial_distribution const& rhs) {
|
|
return !(lhs == rhs);
|
|
}
|
|
};
|
|
} // namespace random
|
|
|
|
using sprout::random::binomial_distribution;
|
|
} // namespace sprout
|
|
|
|
#endif // #ifndef SPROUT_RANDOM_BINOMIAL_DISTRIBUTION_HPP
|
|
|